So why exactly does forward euler cause an increase in energy and backward euler cause a dampening?
The concept of forward Euler theoretically should would and not create an increase or decrease in Energy. If we were to use this same equation but instead add a cap to the minimum and maximum, can this solve the forward Euler problem? Is there a mathematical proof why this extra energy comes, because it has to come from somewhere (ie double value overflow, rounding errors, max-min)
@merc Check out the slides on "stability analysis" in this slide deck, and feel free to ask again if something still isn't clear!
@dvanmali Likewise, check out the next slide, which shows why forward Euler blows up. You could try artificially capping the velocity (say) to a maximum/minimum value, but this will generally yield motion that can look totally wrong. (You might even try it for A4!)